Errors in medical prescriptions occur and a study1 examined whether electronic p

Question

Errors in medical prescriptions occur and a study1 examined whether electronic prescribing may help reduce errors. Two groups of doctors used written prescriptions and had similar error rates before the study. One group switched to e-prescriptions while the other continued to use written prescriptions, and error rates were measured one year later. The results are given in Table 1. Error No Error Total Electronic 254 3594 3848 Written 1478 2370 3848 Table 1 Are prescription error rates different? Find a 99% confidence interval for the difference in the two proportions, p Subscript w Baseline minus p Subscript e, where p Subscript w is the proportion of errors using written prescriptions and p Subscript e is the proportion of errors using e-prescriptions. Round your answers to three decimal places. The 99% confidence interval is to . Is it plausible that there is no difference?

Explanation / Answer

Solution:

For 99% Confidence Interval

x1 = 1478, n1 = 3848, x2 = 254, n2 = 3848

p1 = x1/n2 = 0.384
p2 = x2/n1 = 0.066
p1-p2 = 0.384 - 0.066 = 0.318
Standard Error = sqrt[p1(1-p1)/n1+p2(1-p2)/n2]
= sqrt[ 0.384(0.616)/3848 + 0.066(0.934)/3848]
= 0.0088

Now Confidence Interval = (p1-p2) ± Z/2 SE
= 0.318 ± 2.575 * 0.0088
= 0.318 ± 0.0227
= [0.2953, 0.3407]

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